#14789: Implement hyperplane arrangements
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Reporter: kcrisman | Owner: sage-combinat
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:38 vbraun]:
> Bit ops are probably best. How about bit-or = `|`:
Out of the binary ops available that's probably the one that makes most
sense. I don't think overloading binops has much precedents in
sage/python, though, so it looks a little odd to me. Given how non-compact
this notation is anyway, do we really need a compact way of combining
hyperplanes?
There's another small problem: vector spaces in sage do not have variable
names. In principle, given a vector space, there is a well-defined set of
all hyperplane arrangements in that space. If we insist on giving names to
the standard basis of the dual vector space, there would be multiple
(determined by the names) and the user would be forced to come up with
names if he/she wants to construct the collection.
I agree that describing a hyperplane in n-space with a tuple of length n+1
feels a little uncomfortable: It should really be a vector in the dual
space together with a scalar, i.e., a pair of an n-tuple and a scalar,
which is awkward to work with by itself.
Would it be better to let (a,b,c,d) mean a*x+b*y+c*z+d=0 (note the sign on
the constant)? That's a little more like standard homogenization.
Precedent in other software dealing with hyperplane arrangements might be
instructive?
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Ticket URL: <http://trac.sagemath.org/ticket/14789#comment:39>
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